An Optimal Mechanism for Sponsored Search Auctions on the Web and Comparison With Other Mechanisms

In this paper, we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we describe two well-known mechanisms for sponsored search auction-Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG). We then derive a new mechanism for sponsored search auction which we call optimal (OPT) mechanism. The OPT mechanism maximizes the search engine's expected revenue, while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We then undertake a detailed comparative study of the mechanisms GSP, VCG, and OPT. We compute and compare the expected revenue earned by the search engine under the three mechanisms when the advertisers are symmetric and some special conditions are satisfied. We also compare the three mechanisms in terms of incentive compatibility, individual rationality, and computational complexity. Note to Practitioners-The advertiser-supported web site is one of the successful business models in the emerging web landscape. When an Internet user enters a keyword (i.e., a search phrase) into a search engine, the user gets back a page with results, containing the links most relevant to the query and also sponsored links, (also called paid advertisement links). When a sponsored link is clicked, the user is directed to the corresponding advertiser's web page. The advertiser pays the search engine in some appropriate manner for sending the user to its web page. Against every search performed by any user on any keyword, the search engine faces the problem of matching a set of advertisers to the sponsored slots. In addition, the search engine also needs to decide on a price to be charged to each advertiser. Due to increasing demands for Internet advertising space, most search engines currently use auction mechanisms for this purpose. These are called sponsored search auctions. A significant percentage of the revenue of Internet giants such as Google, Yahoo!, MSN, etc., comes from sponsored search auctions. In this paper, we study two auction mechanisms, GSP and VCG, which are quite popular in the sponsored auction context, and pursue the objective of designing a mechanism that is superior to these two mechanisms. In particular, we propose a new mechanism which we call the OPT mechanism. This mechanism maximizes the search engine's expected revenue subject to achieving Bayesian incentive compatibility and individual rationality. Bayesian incentive compatibility guarantees that it is optimal for each advertiser to bid his/her true value provided that all other agents also bid their respective true values. Individual rationality ensures that the agents participate voluntarily in the auction since they are assured of gaining a non-negative payoff by doing so.

An iterative auction mechanism for combinatorial exchanges

Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. In this paper, we develop computationally efficient iterative auction mechanisms for solving combinatorial exchanges. Our mechanisms satisfy Individual-rationality (IR) and budget-nonnegativity (BN) properties. We also show that our method is bounded and convergent. Our numerical experiments show that our algorithm produces good quality solutions and is computationally efficient.

Composite auction method for suppressing unreasonable electricity price spikes in a competitive electricity market

The existence of undesirable electricity price spikes in a competitive electricity market requires an efficient auction mechanism. However, many of the existing auction mechanism have difficulties in suppressing such unreasonable price spikes effectively. A new auction mechanism is proposed to suppress effectively unreasonable price spikes in a competitive electricity market. It optimally combines system marginal price auction and pay as bid auction mechanisms. A threshold value is determined to activate the switching between the marginal price auction and the proposed composite auction. Basically when the system marginal price is higher than the threshold value, the composite auction for high price electricity market is activated. The winning electricity sellers will sell their electricity at the system marginal price or their own bid prices, depending on their rights of being paid at the system marginal price and their offers' impact on suppressing undesirable price spikes. Such economic stimuli discourage sellers from practising economic and physical withholdings. Multiple price caps are proposed to regulate strong market power. We also compare other auction mechanisms to highlight the characteristics of the proposed one. Numerical simulation using the proposed auction mechanism is given to illustrate the procedure of this new auction mechanism.

Intraday volatility

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

A winner determination algorithm for multi-unit combinatorial auctions with reserve prices

Combinatorial auction mechanisms have been used in many applications such as resource and task allocation, planning and time scheduling in multi-agent systems, in which the items to be allocated are complementary or substitutable. The winner determination in combinatorial auction itself is a NP-complete problem, and has attracted many attentions of researchers world wide. Some outstanding achievements have been made including CPLEX and CABOB algorithms on this topic. To our knowledge, the research into multi-unit combinatorial auctions with reserve prices considered is more or less ignored. To this end, we present a new algorithm for multi-unit combinatorial auctions with reserve prices, which is based on Sandholm's work. An efficient heuristic function is developed for the new algorithm. Experiments have been conducted. The experimental results show that auctioneer agent can find the optimal solution efficiently for a reasonable problem scale with our algorithm.

Market coupling in the power markets

The thesis analyses the European Unions’ effort to create an integrated pan-European electricity market based on “market coupling” as the proposed allocation mechanism for interconnector transfer capacity. Thus, the thesis’ main focus is if market coupling leads to a price convergence in interlinked markets and how it affects the behavior of electricity price data. The applied research methods are a qualitative, structured literature review and a quantitative analysis of electricity price data. The quantitative analysis relies on descriptive statistics of absolute price differentials and on a Cointegration analysis according to Engle & Granger (1987)’s two step approach. Main findings are that implicit auction mechanisms such as market coupling are more efficient than explicit auctions. Especially the method of price coupling leads to a price convergence in involved markets, to social welfare gains and reduces market power of producers, as shown on the example of the TLC market coupling. The market coupling initiative between Germany and Denmark, on the other hand, is evaluated as less successful and illustrates the complexity and difficulties of implementing market coupling initiatives. The cointegration analysis shows that the time series were already before the coupling date cointegrated, but the statistical significance increased. The thesis suggests that market coupling leads to a price convergence of involved markets and thus functions as method to create a single, integrated European electricity market.

Design of an optimal auction for sponsored search auctions

In this paper we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we design a novel auction which we call the OPT (optimal) auction. The OPT mechanism maximizes the search engine's expected revenue while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We show that the OPT mechanism is superior to two of the most commonly used mechanisms for sponsored search namely (1) GSP (Generalized Second Price) and (2) VCG (Vickrey-Clarke-Groves). We then show an important revenue equivalence result that the expected revenue earned by the search engine is the same for all the three mechanisms provided the advertisers are symmetric and the number of sponsored slots is strictly less than the number of advertisers.

Multi-Armed Bandit Mechanisms for Multi-Slot Sponsored Searth Auctions

In pay-per click sponsored search auctions which are currently extensively used by search engines, the auction for a keyword involves a certain number of advertisers (say k) competing for available slots (say m) to display their ads. This auction is typically conducted for a number of rounds (say T). There are click probabilities mu_ij associated with agent-slot pairs. The search engine's goal is to maximize social welfare, for example, the sum of values of the advertisers. The search engine does not know the true value of an advertiser for a click to her ad and also does not know the click probabilities mu_ij s. A key problem for the search engine therefore is to learn these during the T rounds of the auction and also to ensure that the auction mechanism is truthful. Mechanisms for addressing such learning and incentives issues have recently been introduced and would be referred to as multi-armed-bandit (MAB) mechanisms. When m = 1,characterizations for truthful MAB mechanisms are available in the literature and it has been shown that the regret for such mechanisms will be O(T^{2/3}). In this paper, we seek to derive a characterization in the realistic but nontrivial general case when m > 1 and obtain several interesting results.

Truthful multi-armed bandit mechanisms for multi-slot sponsored search auctions

In pay-per-click sponsored search auctions which are currently extensively used by search engines, the auction for a keyword involves a certain number of advertisers (say k) competing for available slots (say m) to display their advertisements (ads for short). A sponsored search auction for a keyword is typically conducted for a number of rounds (say T). There are click probabilities mu(ij) associated with each agent slot pair (agent i and slot j). The search engine would like to maximize the social welfare of the advertisers, that is, the sum of values of the advertisers for the keyword. However, the search engine does not know the true values advertisers have for a click to their respective advertisements and also does not know the click probabilities. A key problem for the search engine therefore is to learn these click probabilities during the initial rounds of the auction and also to ensure that the auction mechanism is truthful. Mechanisms for addressing such learning and incentives issues have recently been introduced. These mechanisms, due to their connection to the multi-armed bandit problem, are aptly referred to as multi-armed bandit (MAB) mechanisms. When m = 1, exact characterizations for truthful MAB mechanisms are available in the literature. Recent work has focused on the more realistic but non-trivial general case when m > 1 and a few promising results have started appearing. In this article, we consider this general case when m > 1 and prove several interesting results. Our contributions include: (1) When, mu(ij)s are unconstrained, we prove that any truthful mechanism must satisfy strong pointwise monotonicity and show that the regret will be Theta T7) for such mechanisms. (2) When the clicks on the ads follow a certain click precedence property, we show that weak pointwise monotonicity is necessary for MAB mechanisms to be truthful. (3) If the search engine has a certain coarse pre-estimate of mu(ij) values and wishes to update them during the course of the T rounds, we show that weak pointwise monotonicity and type-I separatedness are necessary while weak pointwise monotonicity and type-II separatedness are sufficient conditions for the MAB mechanisms to be truthful. (4) If the click probabilities are separable into agent-specific and slot-specific terms, we provide a characterization of MAB mechanisms that are truthful in expectation.

Agent-orientated auction mechanism and strategy design

Agent-based technology is playing an increasingly important role in today’s economy. Usually a multi-agent system is needed to model an economic system such as a market system, in which heterogeneous trading agents interact with each other autonomously. Two questions often need to be answered regarding such systems: 1) How to design an interacting mechanism that facilitates efficient resource allocation among usually self-interested trading agents? 2) How to design an effective strategy in some specific market mechanisms for an agent to maximise its economic returns? For automated market systems, auction is the most popular mechanism to solve resource allocation problems among their participants. However, auction comes in hundreds of different formats, in which some are better than others in terms of not only the allocative efficiency but also other properties e.g., whether it generates high revenue for the auctioneer, whether it induces stable behaviour of the bidders. In addition, different strategies result in very different performance under the same auction rules. With this background, we are inevitably intrigued to investigate auction mechanism and strategy designs for agent-based economics. The international Trading Agent Competition (TAC) Ad Auction (AA) competition provides a very useful platform to develop and test agent strategies in Generalised Second Price auction (GSP). AstonTAC, the runner-up of TAC AA 2009, is a successful advertiser agent designed for GSP-based keyword auction. In particular, AstonTAC generates adaptive bid prices according to the Market-based Value Per Click and selects a set of keyword queries with highest expected profit to bid on to maximise its expected profit under the limit of conversion capacity. Through evaluation experiments, we show that AstonTAC performs well and stably not only in the competition but also across a broad range of environments. The TAC CAT tournament provides an environment for investigating the optimal design of mechanisms for double auction markets. AstonCAT-Plus is the post-tournament version of the specialist developed for CAT 2010. In our experiments, AstonCAT-Plus not only outperforms most specialist agents designed by other institutions but also achieves high allocative efficiencies, transaction success rates and average trader profits. Moreover, we reveal some insights of the CAT: 1) successful markets should maintain a stable and high market share of intra-marginal traders; 2) a specialist’s performance is dependent on the distribution of trading strategies. However, typical double auction models assume trading agents have a fixed trading direction of either buy or sell. With this limitation they cannot directly reflect the fact that traders in financial markets (the most popular application of double auction) decide their trading directions dynamically. To address this issue, we introduce the Bi-directional Double Auction (BDA) market which is populated by two-way traders. Experiments are conducted under both dynamic and static settings of the continuous BDA market. We find that the allocative efficiency of a continuous BDA market mainly comes from rational selection of trading directions. Furthermore, we introduce a high-performance Kernel trading strategy in the BDA market which uses kernel probability density estimator built on historical transaction data to decide optimal order prices. Kernel trading strategy outperforms some popular intelligent double auction trading strategies including ZIP, GD and RE in the continuous BDA market by making the highest profit in static games and obtaining the best wealth in dynamic games.

A dynamic pricing reverse auction-based resource allocation mechanism in cloud workflow systems

Market-oriented reverse auction is an efficient and cost-effective method for resource allocation in cloud workflow systems since it can dynamically allocate resources depending on the supply-demand relationship of the cloud market. However, during the auction the price of cloud resource is usually fixed, and the current resource allocation mechanisms cannot adapt to the changeable market properly which results in the low efficiency of resource utilization. To address such a problem, a dynamic pricing reverse auction-based resource allocation mechanism is proposed. During the auction, resource providers can change prices according to the trading situation so that our novel mechanism can increase the chances of making a deal and improve efficiency of resource utilization. In addition, resource providers can improve their competitiveness in the market by lowering prices, and thus users can obtain cheaper resources in shorter time which would decrease monetary cost and completion time for workflow execution. Experiments with different situations and problem sizes are conducted for dynamic pricing-based allocation mechanism (DPAM) on resource utilization and the measurement of Time∗Cost (TC). The results show that our DPAM can outperform its representative in resource utilization, monetary cost, and completion time and also obtain the optimal price reduction rates.

Batch Verification of Validity of Bids in Homomorphic E-auction

Bid opening in e-auction is efficient when a homomorphic secret sharing function is employed to seal the bids and homomorphic secret reconstruction is employed to open the bids. However, this high efficiency is based on an assumption: the bids are valid (e.g., within a special range). An undetected invalid bid can compromise correctness and fairness of the auction. Unfortunately, validity verification of the bids is ignored in the auction schemes employing homomorphic secret sharing (called homomorphic auction in this paper). In this paper, an attack against the homomorphic auction in the absence of bid validity check is presented and a necessary bid validity check mechanism is proposed. Then a batch cryptographic technique is introduced and applied to improve the efficiency of bid validity check.

A Multiplicative Homomorphic Sealed-Bid Auction-Based on Goldwasser-Micali Encryption

Instead of the costly encryption algorithms traditionally employed in auction schemes, efficient Goldwasser-Micali encryption is used to design a new sealed-bid auction. Multiplicative homomorphism instead of the traditional additive homomorphism is exploited to achieve security and high efficiency in the auction. The new scheme is the currently known most efficient non-interactive sealed-bid auction with bid privacy.